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MTO 20.2: Wild, Vicentino's 31-Tone Compositional Theory

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MTO 20.2: Wild, Vicentino's 31-Tone Compositional Theory Volume 20, Number 2, June 2014 Copyright © 2014 Society for Music Theory Genus, Species and Mode in Vicentino’s 31-tone Compositional Theory Jonathan Wild NOTE: The examples for the (text-only) PDF version of this item are available online at: http://www.mtosmt.org/issues/mto.14.20.2/mto.14.20.2.wild.php KEYWORDS: Vicentino, enharmonicism, chromaticism, sixteenth century, tuning, genus, species, mode ABSTRACT: This article explores the pitch structures developed by Nicola Vicentino in his 1555 treatise L’Antica musica ridotta alla moderna prattica . I examine the rationale for his background gamut of 31 pitch classes, and document the relationships among his accounts of the genera, species, and modes, and between his and earlier accounts. Specially recorded and retuned audio examples illustrate some of the surviving enharmonic and chromatic musical passages. Received February 2014 Table of Contents Introduction [1] Tuning [4] The Archicembalo [8] Genus [10] Enharmonic division of the whole tone [13] Species [15] Mode [28] Composing in the genera [32] Conclusion [35] Introduction [1] In his treatise of 1555, L’Antica musica ridotta alla moderna prattica (henceforth L’Antica musica ), the theorist and composer Nicola Vicentino describes a tuning system comprising thirty-one tones to the octave, and presents several excerpts from compositions intended to be sung in that tuning. (1) The rich compositional theory he develops in the treatise, in concert with the few surviving musical passages, offers a tantalizing glimpse of an alternative pathway for musical development, one whose radically augmented pitch materials make possible a vast range of novel melodic gestures and harmonic successions. In this article I begin with an acoustic derivation of the 31-tone scale, a derivation that is not entirely explicit in L’Antica musica . I go on to examine the aesthetic rationales Vicentino proposes for his tuning system, and to investigate, through close reading of the treatise, the modal and generic frameworks that he develops within it, while considering their historical antecedents. Finally I consider to what extent these pre-compositional pitch structures are realized in the surviving compositions by performing some preliminary analysis on the works excerpted in the treatise. I shall not attempt an exhaustive account of Vicentino’s advice for composers, which encompasses rhetoric, text setting, and affect; my focus will remain on the novel pitch structures his theories generate. 1 of 19 [2] One difficulty in working with a repertoire such as this is the inability of the modern musician to recreate, mentally or in performance, the sound and affect of the unfamiliar intervals from the enharmonic genus. In my own experience I found I needed to hear what Vicentino intended before fully grasping what was at stake in his theorizing or appreciating the import of the musical possibilities. Renderings accomplished via synthesis remained musically unsatisfying. And so with the help of my colleague Peter Schubert I have created aural illustrations of the musical examples by retuning, in post-production, specially recorded performances by professional singers to match precisely the intonational stipulations in L’Antica musica .(2) Some of these recordings appear as audio examples in this article. [3] I reserve for a follow-up article to this one, to be published separately, a more thorough analysis of the surviving compositions, not restricting myself to the theoretical approaches suggested by Vicentino’s own writings in L’Antica musica . Additionally, in this second article I shall venture beyond Vicentino’s compositions and investigate the results of applying the practices demonstrated in his enharmonic works to some carefully selected music by a near-contemporary, Luzzasco Luzzaschi. Tuning [4] As was well known by Vicentino’s lifetime, the compound major 3rd derived by stacking four perfect 5ths is too wide when compared to the major 3rd of just intonation, now known to be derived from the harmonic series. The discrepancy between the two, 21.506 cents, is the syntonic comma. (3) For keyboard instruments the practical solution to the incommensurability of 5ths and 3rds, if pure major 3rds were desired, was to narrow each perfect 5th by a small amount—one quarter of the syntonic comma—causing a stack of four 5ths to yield a pure major 3rd. The resulting temperament is called ¼-comma meantone—or often simply meantone—due to the size of its whole tone, which is the mean of the 9:8 and 10:9 whole tones first described in Ptolemy’s syntonic diatonic and proposed in several earlier sixteenth- century treatises. (4) [5] If this temperament is extended to a chain of 12 pitches, all related by meantone 5ths of 696.578 cents, some pitches near the ends of the chain will not be suitable as triadic roots, since the triad’s third or fifth, or both, will be noticeably mistuned. As an example, if the chain runs from E at its flatmost to G at its sharpmost—the most common arrangement—then B major is one such mistuned triad, as only an E is available, and not the correct D . If the chain is extended sharpwards by one 5th, then both pitches, E and D , may be present simultaneously, and keyboard instruments that employed split keys such as D /E were not uncommon in Italy in the sixteenth century. (5) Such an instrument, accommodating more than twelve pitches per octave, augments the usable tonal region so as to encompass more remote keys. [6] The tuning system Vicentino intended for his vocal compositions is founded on a fortuitous coincidence: in ¼-comma meantone temperament, the discrepancy between the pitches D and E (or any other pair that are enharmonically equivalent in 12-tone equal temperament—i.e., any pair lying twelve steps distant from one another in a chain of perfect 5ths) is almost exactly one fifth of the whole tone; the two pitches lie respectively two fifths and three fifths of a tone above D. (6) This suggests the possibility of interposing additional pitches, at one fifth and at four fifths of a tone above D, so as to divide the whole tone into five equal parts. The pitch midway between D and D is notated in Vicentino’s musical examples as a D with a dot above the notehead; the dot indicates a raise in pitch of a fifth-tone. In the present article I use a convention adapted from this musical notation and write a superscript dot above the letter-name for these inflected pitches, thus: Ḋ. The remaining pitch, between E and E , is notated as Ė .(7) Figure 1 illustrates the resulting complete subdivision of the D–E whole tone and shows the correspondence of the dotted pitches to their less exotic double-flat and double-sharp equivalents. (8) The chromatic semitones D–D and E –E are each two fifth-tones in size, and the diatonic semitones D–E and D –E span three fifth-tones. It follows that the natural diatonic semitones E–F and B–C must also span three fifth-tones (the subdivision of E–F is also shown in Figure 1 ). Thus the octave, which the diatonic scale dissects into five whole tones and two diatonic semitones, ends up comprising 31 steps: 5×5 + 2×3 = 31. (9) Vicentino identifies the step size of this 31-fold division of the octave with the smallest steps of the Greek enharmonic genus, leading to its appellation of enharmonic diesis. (10) [7] The preceding paragraph gave one derivation for the 31-fold division of the octave, beginning with the near correspondence of the enharmonic diesis to one fifth of a meantone whole tone. But we can make use of a different principle, that of the quasi-closed cycle of 5ths, to reach the same result. A set of twelve pitches generated by iterating meantone-tempered 5ths does not “wrap around” with a usable 5th: the interval between the end of the chain and its beginning, a so-called “wolf 5th,” is too wide at about 737 cents. If we search for longer chains, generated by iterating the meantone 5th more than twelve times, that also wrap around with a 5th-like interval, we shall find that after 19 pitches a narrow wolf 5th of about 661 cents is left over. Concatenating the two chains, we find that the opposite errors of the 12-note and 19-note chains neatly cancel out, and the 31-note chain of meantone 5ths results in a very nearly closed cycle with a wrap-around 5th of 702.65 cents—not what we would typically call a wolf, as it is considerably closer to a pure 5th (701.955 cents) than is the meantone 5th used to generate the rest of the cycle! (11) [8] To within the small errors discussed in note 10, then, Vicentino’s system circulates; that is, a complete circle of 31 keys 2 of 19 may be traversed without encountering any unusable, out-of-tune triads. He writes of the archicembalo—the special harpsichord he invented, which includes all 31 pitches in each octave—that it is “the foremost and perfect instrument, in that none of the keys lacks any consonances” (315). (12) While Vicentino thus recognizes the circulating nature of an entire 31-tone system, this does not seem to have been his foremost rationale for proposing it. In the surviving musical excerpts he never uses triads or keys from opposite ends of the 31-tone chain of 5ths in close proximity to one another, and so the tuning does not need to circulate and no potential “wolf ” intervals arise. This renders moot the question of whether he intended his 31-tone tuning to be exactly equal, or merely to yield a good approximation of equality.
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